OCR MEI Further Pure Core AS 2023 June — Question 7

Exam BoardOCR MEI
ModuleFurther Pure Core AS (Further Pure Core AS)
Year2023
SessionJune
TopicComplex numbers 2

  1. By expanding \(( \sqrt { 3 } + \mathrm { i } ) ^ { 5 }\), express \(z ^ { 5 }\) in the form \(\mathrm { a } +\) bi where \(a\) and \(b\) are real and exact.
    1. Express \(z\) in modulus-argument form.
    2. Hence find \(z ^ { 5 }\) in modulus-argument form.
    3. Use this result to verify your answers to part (a).